In the last decade, traditional dictionary learning methods have been successfully applied to various pattern classification tasks. Although these methods produce sparse representations of signals which are robust against distortions and missing data, such representations quite often turn out to be unsuitable if the final objective is signal classification. In order to overcome, or at least to attenuate, such a weakness, several new methods which incorporate discriminant information into sparse-inducing models have emerged in recent years. In particular, methods for discriminant dictionary learning have shown to be more accurate than the traditional ones, which are only focused on minimizing the total representation error. In this work, we present both a novel multi-class discriminant measure and an innovative dictionary learning method. For a given dictionary, this new measure, which takes into account not only when a particular atom is used for representing signals coming from a certain class and the magnitude of its corresponding representation coefficient, but also the effect that such an atom has in the total representation error, is capable of efficiently quantifying the degree of discriminability of each one of the atoms. On the other hand, the new dictionary construction method yields dictionaries which are highly suitable for multi-class classification tasks. Our method was tested with two widely used databases for handwritten digit recognition and for object recognition, and compared with three state-of-the-art classification methods. The results show that our method significantly outperforms the other three achieving good recognition rates and additionally, reducing the computational cost of the classifier.

在过去的十年中，传统的字典学习方法已成功地应用于各种模式分类任务。尽管这些方法产生的信号的稀疏表示形式对失真和丢失数据具有鲁棒性，但如果最终目标是信号分类，则这种表示形式通常会不合适。为了克服或至少减轻这种弱点，近年来出现了几种将判别信息纳入稀疏诱导模型的新方法。尤其是，用于区分词典学习的方法已显示出比传统方法更为准确，传统方法仅专注于最大程度地减少总表示误差。在这项工作中，我们同时提出了一种新颖的多类判别方法和一种创新的词典学习方法。对于给定的字典，这种新的度量不仅考虑到当特定原子用于表示来自某一类的信号及其相应表示系数的大小时，而且还考虑了这种原子在总数中的作用。表示误差，能够有效地量化每个原子的可分辨程度。另一方面，新的字典构造方法产生的字典非常适​​合于多类分类任务。我们的方法在两个广泛使用的手写数字识别和对象识别数据库中进行了测试，并与三种最新的分类方法进行了比较。结果表明，我们的方法明显优于其他三个方法，具有良好的识别率，此外，